Logistic Regression: Sampling Methods and Analysis
Logistic
Simple Random Sample
An observation on a binary outcome variable y and p
independent variables x1, x2, xp are obtained from each of n
subjects or units selected completely at random from a
popu
6.1 - Inference for the Binomial Parameter: Population Proportion
RECALL: If np5 and n(1p)5 then
^p is approximately normal with mean and sd:
p ( 1 p )
n
One-sample Z-interval for the population proportion, p.
1.
Assumptions needed to check before one can
It all begins with Y
wi
th
X
y
Lin
e
ar
t
re
nd
Use Y values to
compute b0 and b1
Least squares line
^
y b0
bx
1
y
pr
ed
es
tim
at
es
And continues with
^
i ct
s
Y = 0 + 1x +
^
y Essentially performs two tasks:
Estimates the mean of Y for a specific x
Test1 Review
Learning objectives and Outcomes for lessons 1 to 6 is an excellent guide to
prepare for this test. You may find the following key words/phrases useful .
Parameters, estimates, residuals and their properties, least squares criterion,
best fit
It all begins with Y
wi
th
X
y
Lin
e
ar
t
re
nd
Use Y values to
compute b0 and b1
Least squares line
^
y b0
bx
1
y
pr
ed
es
tim
at
es
And continues with
^
i ct
s
Y = 0 + 1x +
^
y Essentially performs two tasks:
Estimates the mean of Y for a specific x
Lesson 4 Review - Detection of LINE assumptions
violations , outliers and model inadequacy.
Method: Residual Analysis using plots
residual vs fit detects
Non linearity
Unequal variances
Outliers
2. residual vs order detects
Non independence
normal probab
Lesson 5. Multiple Linear Regression(MLR)
- Review
Here we extended the SLR equation to include several
predictor variables.
Matrix form is a convenient way to work with MLR
Y=X +
Recall
how you can write the data values into Y and X respectively.
X is c
Lesson 1
Least Square Criterion says to "minimize the sum of the squared prediction errors.
What does b0 tell us? If x=0 is within the scope of the model, then b0 is the predicted mean
response when x = 0. Otherwise, b0 is not meaningful.
What does b1 te
4.1 - Discrete Probability Distributions
Expected value of X:
Variance of X:
E ( X )= P ( xi )( x i)
2
2
Var ( X )= P(x i )( xi )[ E ( X ) ]
4.2 - Binomial Distributions
A special discrete random variable is the binomial. We have a binomial experiment if
Binary Outcome Variable
Binary Data
The observed value of a variable Y for each unit falls into one of
two categories (success/failure; alive/dead; positive/negative)
conveniently coded as 0 (=nonevent) and 1 (=event).
Observed outcome y from each unit
Analysis of binary outcome variable Case for a model
Analysis
Example - ICU Data
Looked at the mortality (STA) rate ignoring all factors that affect STA;
One sample proportion problem (estimation and test)
Looked at the association between admission (
Multiple Logistic Regression Model
Mathematical representation of the relationship between a
binary outcome variable and a set of p covariates
Multiple Linear Logistic Regression
Suppose we have a sample of n independent observations (y i, x1i, ,
xpi),
Multinomial Logistic Regression
Multinomial
Example 1. Health Insurance Plans
Employees are asked to choose one of three plans (say 0, 1, 2).
The outcome variable Y (employees choice) is nominal with three
categories, distribution of Y is tri-nomial wit
Chapter Five: Assessing the Fit of the model
A model is considered a good fit to the data if
summary measures of the distance between observed y and predicted y are
small
the contribution of each pair (observed y, predicted y) to summary
measures is un
Multiple Logistic Regression Model
Binary outcome, several quantitative/qualitative
independent variables x1, x2, xk
(x)=exp(g(x)/(1+exp(g(x)
Logit(x) = ln(x)/(1-(x)= g(x)
Two problems that need to be addressed are
Determine the functional form for g
Tentative Course Schedule: Stat 500 Fall 2015
Getting Started
Complete the activities in the Getting Started folder (see the Lessons tab) by
August 28th
Read Proctor Information Form (Final Only) and start working on this.
Lesson 1 (Monday August 24th t